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The Neumann problem on the domain in š3 bounded by the Clifford torus
Advanced Nonlinear Studies, 2023 In this study, the solution of the Neumann problem associated with the CR Yamabe operator on a subset Ī©\Omega of the CR manifold S3{{\mathbb{S}}}^{3} bounded by the Clifford torus Ī£\Sigma is discussed.
Case Jeffrey S. +4 more
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Results in Applied Mathematics, 2021 We consider a nonlinear partial differential equation of Yamabe-type. In Boucheche (2019), it has been proved that the problem admits a solution under the assumption that the gradient of the associated variational functional is lower bounded by a ...
Khadijah Sharaf
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Surveys in Differential Geometry, 2012 1.1. The k-Yamabe problem. The k-Yamabe problem is a higher order extension of the celebrated Yamabe problem for scalar curvature. It was initially proposed by Viaclovsky [72] and also arose in the study of Q-curvatures in [11]. Viaclovsky found that in a conformal metric, the resultant k-curvature equation can be expressed as an equation similar to ...
Sheng, Weimin +2 more
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Advanced Engineering Materials, Volume 25, Issue 24, December 2023., 2023 The deliberate control of crystallographic texture in components using the laser powder bed fusion (LPBF) process is a material design and processing concept gaining interest in recent years. This review presents the influence of the LPBF process parameters on the melting mode, melt pool shape, texture, and microstructural evolution, and the effects of
Prince Valentine Cobbinah +2 more
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Kodaira dimension and the Yamabe problem, II
Communications in Analysis and Geometry, 2023 25 pages ...
Albanese, Michael, LeBrun, Claude
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On harmonic and biharmonic maps from gradient Ricci solitons
Mathematische Nachrichten, Volume 296, Issue 11, Page 5109-5122, November 2023., 2023 Abstract We study harmonic and biharmonic maps from gradient Ricci solitons. We derive a number of analytic and geometric conditions under which harmonic maps are constant and which force biharmonic maps to be harmonic. In particular, we show that biharmonic maps of finite energy from the twoādimensional cigar soliton must beĀ harmonic.
Volker Branding
wiley +1 more source
Existence and Uniqueness of Green's Functions to Nonlinear Yamabe Problems
Communications on Pure and Applied Mathematics, Volume 76, Issue 8, Page 1554-1607, August 2023., 2023 Abstract For a given finite subset S of a compact Riemannian manifold (M,g) whose Schouten curvature tensor belongs to a given cone, we establish a necessary and sufficient condition for the existence and uniqueness of a conformal metric on M\S such that each point of S corresponds to an asymptotically flat end and that the Schouten tensor of the ...
Yanyan Li, Luc Nguyen
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Monopole metrics and the orbifold Yamabe problem [PDF]
, 2010 We consider the self-dual conformal classes on n#CP^2 discovered by LeBrun. These depend upon a choice of n points in hyperbolic 3-space, called monopole points.
Viaclovsky, Jeff
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A fully nonlinear version of the Yamabe problem and a Harnack type inequality [PDF]
, 2002 We present some results on a fully nonlinear version of the Yamabe problem and a Harnack type inequality for general conformally invariant fully nonlinear second order elliptic ...
Li, Aobing, Li, Yanyan
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A Problem Concerning Yamabe-Type Operators of Negative Admissible Metrics
Journal of Applied Mathematics, 2012 This paper is about a problem concerning nonlinear Yamabe-type operators of negative admissible metrics. We first give a result on Ļk Yamabe problem of negative admissible metrics by virtue of the degree theory in nonlinear functional analysis and the ...
Jin Liang, Huan Zhu
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